Velocity Amplitudes in Global Convection Simulations: The Role of the Prandtl Number and Near-Surface Driving

Abstract

Several lines of evidence suggest that the velocity amplitude in global simulations of solar convection, U, may be systematically over-estimated. Motivated by these recent results, we explore the factors that determine U and we consider how these might scale to solar parameter regimes. To this end, we decrease the thermal diffusivity $\kappa$ along two paths in parameter space. If the kinematic viscosity $\nu$ is decreased proportionally with $\kappa$ (fixing the Prandtl number $P_r=\nu /\kappa$), we find that U increases but asymptotes toward a constant value, as found by Featherstone & Hindman (2016). However, if $\nu$ is held fixed while decreasing $\kappa$ (increasing $P_r$), we find that U systematically decreases. We attribute this to an enhancement of the thermal content of downflow plumes, which allows them to carry the solar luminosity with slower flow speeds. We contrast this with the case of Rayleigh-Benard convection which is not subject to this luminosity constraint. This dramatic difference in behavior for the two paths in parameter space (fixed $P_r$ or fixed $\nu$) persists whether the heat transport by unresolved, near-surface convection is modeled as a thermal conduction or as a fixed flux. The results suggest that if solar convection can operate in a high-$P_r$ regime, then this might effectively limit the velocity amplitude. Small-scale magnetism is a possible source of enhanced viscosity that may serve to achieve this high-$P_r$ regime.

arXiv comment34 Pages, 8 Figures, submitted to a special issue of "Advances in Space Research" on "Solar Dynamo Frontiers"

References in corpus (22)

• Large scale dynamics in turbulent Rayleigh-Benard convection
• Global-Scale Turbulent Convection and Magnetic Dynamo Action in the Solar Envelope
• From solar-like to anti-solar differential rotation in cool stars
• Anomalously Weak Solar Convection
• Magnetic Wreaths and Cycles in Convective Dynamos
• Meridional Circulation in Solar and Stellar Convection Zones
• A simulation of convective dynamo in the solar convective envelope: maintenance of the solar-like differential rotation and emerging flux
• Differential rotation in solar-like stars from global simulations
• Grand Minima and Equatorward Propagation in a Cycling Stellar Convective Dynamo
• Seismic Sounding of Convection in the Sun
• Magnetically controlled stellar differential rotation near the transition from solar to anti-solar profiles
• High-resolution calculation of the solar global convection with the reduced speed of sound technique: II. Near surface shear layer with the rotation
• Confirmation of bistable stellar differential rotation profiles
• The Spectral Amplitude of Stellar Convection and its Scaling in the High-Rayleigh-Number Regime
• Helioseismic Imaging of Fast Convective Flows Throughout the Near-Surface Shear Layer
• Turbulent Rayleigh-Bénard convection in spherical shells
• High-resolution calculations of the solar global convection with the reduced speed of sound technique: I. The structure of the convection and the magnetic field without the rotation
• On the Amplitude of Convective Velocities in the Deep Solar Interior
• Efficient small-scale dynamo in solar convection zone
• The Role of Subsurface Flows in Solar Surface Convection: Modeling the Spectrum of Supergranular and Larger Scale Flows
• Seismic Constraints on Interior Solar Convection
• Convection in stellar envelopes: a changing paradigm

Cited by in corpus (32)

• Advances in mean-field dynamo theory and applications to astrophysical turbulence
• Solar differential rotation reproduced with high-resolution simulation
• Generation solar-like differential rotation
• Supergranulation as the largest buoyantly driven convective scale of the Sun
• Consequences of high effective Prandtl number on solar differential rotation and convective velocity
• On a new formulation for energy transfer between convection and fast tides with application to giant planets and solar type stars
• Effects of a subadiabatic layer on convection and dynamos in spherical wedge simulations
• Theory of solar oscillations in the inertial frequency range: Amplitudes of equatorial modes from a nonlinear rotating convection simulation
• Convective velocity suppression via the enhancement of subadiabatic layer: Role of the effective Prandtl number
• Revisiting the Sun's Strong Differential Rotation along Radial Lines
• Driving Solar Giant Cells through the Self-Organization of Near-Surface Plumes
• Entropy Rain: Dilution and Compression of Thermals in Stratified Domains
• Solar-like to Antisolar Differential Rotation: A Geometric Interpretation
• Exploring Bistability in the Cycles of the Solar Dynamo through Global Simulations
• Prandtl number dependence of compressible convection: Flow statistics and convective energy transport
• Incorporating Surface Convection into a 3D Babcock-Leighton Solar Dynamo Model
• Breaking Taylor-Proudman balance by magnetic field in stellar convection zone
• Physically motivated heat conduction treatment in simulations of solar-like stars: effects on dynamo transitions
• Small-Scale Dynamo in Stably Stratified Turbulence
• Prandtl-Number Effects in High-Rayleigh-Number Spherical Convection
• Depth Dependent Dynamics Explain the Equatorial Jet Difference Between Jupiter and Saturn
• Global Turbulent Solar Convection: a Numerical Path Investigating Key Force Balances in the context of the Convective Conundrum
• Simulations of entropy rain-driven convection
• Turbulent Prandtl number from isotropically forced turbulence
• Impacts of small-scale dynamo on rotating columnar convection in stellar convection zones
• 3D Simulations and MLT: II. Onsager's Ideal Turbulence
• Spatial inhomogeneity of kinetic and magnetic dissipations in thermal convection
• Scale-resolved turbulent Prandtl number for Rayleigh-Bénard convection at $\mathbf{Pr}=10^{-3}$
• Scale-dependent analysis of angular momentum flux in high-resolution magnetohydrodynamic simulations for solar differential rotation
• Differential rotation in convecting spherical shells with non-uniform viscosity and entropy diffusivity
• Solar-like dynamos and rotational scaling of cycles from star-in-a-box simulations
• Confinement of the Solar Tachocline by Dynamo Action in the Radiative Interior